It is known to provide flareless tube couplings having a one piece ferrule or sleeve which, at its axially inner end, is radially contracted by a body cam surface into sealed engagement with the body cam surface and into gripping and sealing engagement with the tube and which, at its axially outer end, has several axially extending slots to provide for contraction of the axially outer end portion of the sleeve by a nut cam surface into gripping engagement with the tube. In such construction, the axial slots must extend axially inwardly a substantial distance beyond the nut cam surface to enable bending of the arcuate fingers into gripping engagement with the tube at a region axially outwardly from the axially inner tube gripping and sealing end of the sleeve. Furthermore, it is difficult to bend the arcuate fingers to a progressively shorter radius as they are bent inwardly into tube gripping engagement.